Is it possible to train the neural network to solve math equations?
Yes, it has been done!

However, the applications aren't to replace calculators or anything like that. The lab I'm associated with develops neural network models of equational reasoning to better understand how humans might solve these problems. This is a part of the field known as Mathematical Cognition. Unfortunately, our website isn't terribly informative, but here's a link to an example of such work.

Apart from that, recent work on extending neural networks to include external memory stores (e.g. Neural Turing Machines) tend to use solving math problems as a good proof of concept. This is because many arithmetic problems involve long procedures with stored intermediate results. See the sections of this paper on long binary addition and multiplication.